Does Europe tax diesel the same way no matter where it's used? I know in the US diesel for generators is exempt from a lot of taxes resulting in it being significantly cheaper in some states.

I only know of Finland, but here diesel for work machines is much cheaper than diesel for driving.

In the UK Diesel is taxed differently for agricultural usage, it typically has a red dye added to it to indicate it's for agricultural use only. I don't honestly know about generators though.

You can use red diesel in a generator, I think the legality comes down to whether it's being used to power a vehicle on a public road.

You're right, some countries have exceptions. Netherlands where I live used to, but no longer does. Not sure about France.